Consider a portfolio with weights of .7 in stocks and .3 in bonds.

		Rate of Return
Scenario	Probability	Stocks		Bonds
Recession	.20	−7	%	+20	%
Normal economy	.60	+22		+11
Boom	.20	+33		+7

Consider a portfolio with weights of .7 in stocks and .3 in bonds.

a.	What is the rate of return on the portfolio in each scenario? (Do not round intermediate calculations. Round your answers to 1 decimal place.)

Scenario	Rate of Return
Recession	%
Normal economy	%
Boom	%

b.	What are the expected rate of return and standard deviation of the portfolio? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Expected rate of return	%
Standard deviation	%

c.	Which investment would you prefer?
	Portfolio

Explanation:

Some values below may show as rounded for display purposes, though unrounded numbers should be used for the actual calculations.

a.

Recession:           (−7% × 0.7) + (20% × 0.3) = 1.1%

Normal economy:  (22% × 0.7) + (11% × 0.3) = 18.7%

Boom:                  (33% × 0.7) + (7% × 0.3) = 25.2%

b.

Expected return = (0.2 × 1.1%) + (0.6 × 18.7%) + (0.2 × 25.2%) = 16.48%

Variance = [0.2 × (1.1 − 16.48)2] + [0.6 × (18.7 − 16.48)2] + [0.2 × (25.2 − 16.48)2] = 65.47

Standard deviation = = 8.09%

c.

rstock = [0.2 × (−7%)] + (0.6 × 22%) + (0.2 × 33%) = 18.40%

rbonds = (0.2 × 20%) + (0.6 × 11%) + (0.2 × 7%) = 12.00%

Variance (stocks) = [0.2 × (−7 − 18.40)2] + [0.6 × (22 − 18.40)2] + [0.2 × (33 − 18.40)2] = 179.44

Standard deviation = = 13.40%

Variance (bonds) = [0.2 × (20 − 12.00)2] + [0.6 × (11 − 12.00)2] + [0.2 × (7 − 12.00)2] = 18.40

Standard deviation = = 4.29%